Optimal path of diffusion over the saddle point and fusion of massive nuclei

Abstract

The diffusion of a particle passing over the saddle point of a two-dimensional quadratic potential is studied via a set of coupled Langevin equations, and the expression for the passing probability is obtained exactly. The passing probability is found to be strongly influenced by the off-diagonal components of inertia and friction tensors. If the system undergoes the optimal path to pass over the saddle point by taking an appropriate direction of initial velocity into account, which departs from the potential valley and has minimum dissipation, the passing probability should be enhanced. Applying this to the fusion of massive nuclei, we show that there exists an optimal injection choice for the deformable target and projectile nuclei, namely, the intermediate deformation between spherical and extremely deformed nuclei, that maximizes the fusion probability.